"One of the nation's best-wired Republicans," as cited by Allen, gave Ryan a better-than 50% chance of leaving the July convention as the party's nominee.

The Republican nominee could be named at the convention if none of the three remaining candidates enter it with 1,237 delegates. Frontrunner Donald Trump needs to secure a bit more than 60% of the remaining delegates to head to the convention with 1,237.

Ryan, who was in Israel as part of a congressional-delegation visit last week, told conservative radio host Hugh Hewitt that he remained uninterested in the job.

"I think you need to run for president if you're going to be president, and I'm not running for president," Ryan said. "So period, end of story."

But, as Allen wrote, Ryan also once insisted he had no interest in becoming the speaker of the House of Representatives.

"In both cases, the maximum leverage is to NOT WANT IT — and to be begged to do it," Allen wrote. "He and his staff are trying to be as Shermanesque as it gets."

AP

The speculation took off in mid-March, after CNBC reported that the Wisconsin lawmaker wouldn't "categorically" rule out accepting the GOP nomination. Ryan has since repeatedly denied that he is seeking the nomination or would accept it from a split convention.

But the House speaker stoked the flames after he gave a late-March speech about the state of American politics, in which he spoke out about the language being used in the presidential race. Though he did not mention any of the candidates by name, Ryan took a shot at Trump by saying that his own party was partially to blame for vitriol in political discourse.

"That was somebody who was laying out the speech that, in most cases, you'd give six months before you announce you're going to run," Allen quoted a Ryan friend as saying.

Ryan's staff later cut a short commercial from the speech that had many asking whether the clip signaled the start of his shadow campaign. His camp shot down that speculation shortly after.

After the speech was announced, a Ryan aide told Business Insider that "he's going to rule himself out and put this to rest once and for all."